Posted - 03/26/2014 : 05:14:30 In an internet article about the globular cluster known as M22 http://www.ask.com/wiki/Messier_22?o=2802&qsrc=999&ad=doubleDown&an=apn&ap=ask.com it is stated that the distance to the object is 10,600 +/- 1,000 light years and that the object subtends an angle in the sky measuring 39 minutes (i.e. 0.65 degree). It is also stated that the size of the object is 99 +/- 9 light years.

Based on what I remember of my high school math I calculate that the size of the object is 120 +/- 11 light years. My calculation is :

Minimum size = sin(0.65) x 9,600 = 108.9 Median size = sin(0.65) x 10,600 = 120.3 Maximum size = sin(0.65) x 11,600 = 131.6

Have I mis-remembered my math?

4 L A T E S T R E P L I E S (Newest First)

Subhotosh Khan

Posted - 06/29/2014 : 10:08:38

quote:Originally posted by daimath

In an internet article about the globular cluster known as M22 http://www.ask.com/wiki/Messier_22?o=2802&qsrc=999&ad=doubleDown&an=apn&ap=ask.com it is stated that the distance to the object is 10,600 +/- 1,000 light years and that the object subtends an angle in the sky measuring 39 minutes (i.e. 0.65 degree). It is also stated that the size of the object is 99 +/- 9 light years.

Based on what I remember of my high school math I calculate that the size of the object is 120 +/- 11 light years. My calculation is :

Minimum size = sin(0.65) x 9,600 = 108.9 Median size = sin(0.65) x 10,600 = 120.3 Maximum size = sin(0.65) x 11,600 = 131.6

Have I mis-remembered my math?

I read the article - and the angle subtended is 32'(=0.009308 rad.).

In that case size indeed is 99 ± 9 lightyears

TchrWill

Posted - 04/04/2014 : 12:06:33 [quote]Originally posted by daimath

In an internet article about the globular cluster known as M22 http://www.ask.com/wiki/Messier_22?o=2802&qsrc=999&ad=doubleDown&an=apn&ap=ask.com it is stated that the distance to the object is 10,600 +/- 1,000 light years and that the object subtends an angle in the sky measuring 39 minutes (i.e. 0.65 degree). It is also stated that the size of the object is 99 +/- 9 light years.

Based on what I remember of my high school math I calculate that the size of the object is 120 +/- 11 light years. My calculation is :

Minimum size = sin(0.65) x 9,600 = 108.9 Median size = sin(0.65) x 10,600 = 120.3 Maximum size = sin(0.65) x 11,600 = 131.6

Based on what I remember of my high school math I calculate that the size of the object is 120 +/- 11 light years. My calculation is :

Minimum size = sin(0.65) x 9,600 = 108.9 Median size = sin(0.65) x 10,600 = 120.3 Maximum size = sin(0.65) x 11,600 = 131.6

As the hill1962 pointed out, the tangent ratio is the proper angle function to use as the cluster diameter D is 2R where

D = 2R[D(tan.325)] resulting in

Minimum D = 2[9600tan.325] = 108.9097 = 108.91 Median D = 2[10600tan.325] = 120.254 = 120.25 = 120 +/-11 Maximum D = 2[11600tan.325] = 131.599 = 131.6

depending on your choice of rounding off rules.

As the hill1962 again points out, big sites often result in big errors. I tried manipulating the numbers around but could not find any path that resulted in a diameter of 99 +/-9. If I find one, I will let you know.

daimath

Posted - 03/26/2014 : 19:52:13 Thanks for taking the time to reply with your confirmation the_hill1962. It is appreciated.

the_hill1962

Posted - 03/26/2014 : 15:26:57 I agree with you. I used the tangent ratio and came up with the same answer. Sorry, I have not checked your work since my answer was the same as yours I figure you set it up correctly (I see you used sine). I have found mistakes on "big" sites also. The most recent was an incorrect statement on wikipedia. I would have written in to correct them but it appeared that you had to register and jump through hoops to make any sort of comments. I hope that you take the time to contact the author of what you found on ask.com